This visualization compares all combinations of initial investments (1, 2, and 4) and annual return rates (1%, 2%, and 4%) over 50 years. All curves follow the same compound-interest logic, but scale and growth rates interact in non-intuitive ways. A higher starting capital shifts the curve upward immediately; a higher return rate steepens it progressively. Over long horizons, return differentials dominate: 1 invested at 4% ultimately overtakes 4 invested at 1%. Early in the horizon, the opposite holds. Time determines when growth rate outweighs initial size. 

Data: Theoretical compound interest growth with annual rates of 1%, 2%, and 4% over 50 years. Initial investment: 1,  2  and 4. Assumes annual compounding with no withdrawals or additional contributions.